Toward an Automated Convergence Tool for Kinetic Monte Carlo Simulation of Conversion, Distributions, and Their Averages in Non-dispersed Phase Linear Chain-Growth Polymerization

Abstract

The time evolution of (bio)chemical processes, specifically those involving distributed species as in polymer synthesis and recycling, can be obtained using Gillespie-based kinetic Monte Carlo simulations, provided that a sufficiently high (Monte Carlo) control volume is utilized with respect to the simulation targets (e.g., focus on only conversion/yield or a combination of the former and average molar masses, or even the combination with complete distributions with accurate tail prediction). For more detailed kinetics and more demanding simulations targets, currently, simulation results are mostly visually checked to decide which control volume to practically use, taking into account user time constraints. The present work puts forward a convergence strategy that avoids relying on subjective visual analysis to set the minimum control value that guarantees the minimization of the stochastic noise for several simulation target combinations to acceptable values. The strategy is illustrated for two (for simplicity, intrinsic) non-dispersed phase bulk chain-growth polymerization processes, one with high average chain lengths and a broad chain length distribution (CLD), that is, free-radical polymerization (FRP), and one with low average chain lengths and a narrow CLD, that is, nitroxide-mediated polymerization (NMP). It is showcased that the monomer conversion profile converges the fastest, with even the occurrence of noise-free simulation results in the absence of numerical convergence. A sufficiently accurate representation of the tail of the (number) CLD in FRP demands a sufficiently high control volume so that relative errors below 0.5% result for the z-based average chain length or molar mass (Mz). This need to inspect Mz convergence further holds under NMP, in general, reversible deactivation radical polymerization (RDRP) conditions, in which it is uncommon to report such higher order averages. An automated convergence check beyond threshold values is recommended to minimize the impact of possible fluctuations in certain simulation targets, specifically peak representations, for example, the initial spike in the dispersity plot in RDRP. The convergence results are supported by the number of radicals in the control volume with values much higher than 2 to accurately represent termination kinetics for specifically CLD prediction, already under intrinsic conditions.